Certainly! Let's solve the given compound inequality step by step.
### Inequality 1: [tex]\(6x + 2 > 14\)[/tex]
1. Subtract 2 from both sides:
[tex]\[
6x + 2 - 2 > 14 - 2
\][/tex]
Simplifying this, we get:
[tex]\[
6x > 12
\][/tex]
2. Divide both sides by 6:
[tex]\[
\frac{6x}{6} > \frac{12}{6}
\][/tex]
Simplifying further, we get:
[tex]\[
x > 2
\][/tex]
### Inequality 2: [tex]\(3x - 1 < 2\)[/tex]
1. Add 1 to both sides:
[tex]\[
3x - 1 + 1 < 2 + 1
\][/tex]
Simplifying this, we get:
[tex]\[
3x < 3
\][/tex]
2. Divide both sides by 3:
[tex]\[
\frac{3x}{3} < \frac{3}{3}
\][/tex]
Simplifying further, we get:
[tex]\[
x < 1
\][/tex]
### Combining the Results:
The solution to the compound inequality [tex]\(6x + 2 > 14\)[/tex] or [tex]\(3x - 1 < 2\)[/tex] is:
[tex]\[
x > 2 \quad \text{or} \quad x < 1
\][/tex]
Hence, the correct choice is:
a. [tex]\(x > 2\)[/tex] or [tex]\(x < 1\)[/tex]
